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Polynomial for secure communicationThank you for your reply. When Bob receives C1 & C2, he decrypts and retrieves m and P(x) and since Bob knows all coeficients of the polynomial and x, he can verify by replacing m in P(x) ... I think that the integrity is provided since the attacker who want to inject C1' corresponding to m' instead of C1, haven't enough information of P(x) to replace the corresponding C2' .... Bob rejects the modified message My question is : with this method, can we provide both confidentiality & integrity of the plaintext m ?

Aug5

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Polynomial for secure communicationthe coefficients are generated by both participants using the same seed. Suppose Alice and Bob share two keys and Alice uses these keys to encrypt m and the result of p(x). Alice --> Bob : C1 = enc(m), C2 = enc(p(x)) Can bob verify the integrity of m using P(x) ?